
das Fell
fur
The dense hair that covers the body of mammals. It protects animals from cold, moisture, and other environmental influences.
Die Katze hat ein sehr weiches, glänzendes Fell.
The cat has very soft, shiny fur.
fur / drumhead
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fur
The dense hair that covers the body of mammals. It protects animals from cold, moisture, and other environmental influences.
Die Katze hat ein sehr weiches, glänzendes Fell.
The cat has very soft, shiny fur.

to fleece someone
An idiom meaning to cheat someone financially, exploit them, or demand an excessive amount of money from them.
Der Verkäufer hat versucht, mir mit dem überteuerten Preis das Fell über die Ohren zu ziehen.
The seller tried to fleece me with the overpriced amount.

drumhead
The membrane stretched over the body of a drum and made to sound by being struck.
Der Schlagzeuger musste vor dem Konzert das Fell seiner Snare-Drum wechseln.
The drummer had to change the drumhead of his snare drum before the concert.
'Das Fell' means animal hair (fur) in German. It is a false friend of the English verb 'fell', the past tense of 'to fall' (in German: 'fiel').
Der Bär hat ein dickes braunes Fell.
The bear has thick brown fur.
In the idiom 'jemandem das Fell über die Ohren ziehen' (to fleece someone), the person being cheated is always in the dative. This is a fixed pattern.
Pass auf, dass sie dir bei dem Autokauf nicht das Fell über die Ohren ziehen.
Be careful that they don't fleece you when you buy the car.
In connection with animal hair, 'Fell' (fur) is often described with adjectives such as 'weich' (soft), 'dicht' (dense), or 'glänzend' (shiny). Typical verbs are 'streicheln' (to stroke), 'bürsten' (to brush), or 'pflegen' (to care for).
Mein Hund verliert im Frühling sehr viel Fell.
My dog loses a lot of fur in spring.
You can always recognize the meaning 'Trommelfell' (drumhead) from the musical context. Words like 'Schlagzeug' (drum kit), 'Trommel' (drum), 'spannen' (to stretch/tighten), 'wechseln' (to change), or 'Instrument' (instrument) make it clear that it is not about animal hair.
Das Fell der großen Trommel ist gerissen.
The drumhead of the bass drum is torn.
skin
For a hairy animal, Haut refers to the outer body organ itself. Fell, by contrast, is the dense hair that covers the body. Haut is therefore used for an injury or irritation, while Fell is used for the color, thickness, or condition of the hair.

Nach dem Regen ist das dichte Fell des Hundes völlig nass.
The dog's thick fur is completely wet after the rain.
Unter den dichten Haaren ist die Haut des Hundes gerötet.
The dog's skin is red under its thick fur.